Covariance and Gramian matrices in control and systems theory.

Covariance and Gramian matrices in control and systems
theory and pattern recognition are studied in the context of
reduction of dimensionality and hence complexity of large-scale
systems. This is achieved by the removal of redundant or
'almost' redundant information contained in the covariance
and Grarrdan matrices. The Karhunen-Loeve expansion (principal
component analysis) and its extensions and the singular value
decomposition of matrices provide the framework for the work
presented in the thesis. The results given for linear dynamical
systems are based on controllability and observability Gramians
and some new developments in singular perturbational analysis
are also presented.